Hand knit socks are worth fixing when a hole develops. Here are my steps to repair a hole on the sole. I begin with matching sock yarn and a tapestry needle to outline the hole with running stitches while the hole is held open on a wooden darning disk.
Next I lay down the long warp threads over which I will weave a patch.
After doing the horizontal weaving, I did some diagonals for reinforcement. Finally, I wove the yarn ends into the sock.
Finished:
It is important to do this as flat as possible, with no knots or bumps.